Optimal inverse of a matrix

Mitra, Sujit Kumar (1975) Optimal inverse of a matrix Sankhya - Series A, 37 (4). pp. 550-563. ISSN 0581-572x

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An optimal approximate solution $(x)$ of the possibly inconsistent equation $Ax=y$ minimizes the norm of $\left( \begin{array}{c} Ax-y \\ x \end{array} \right)$ considered as a vector in an appropriate product space. Such a solution is computed as $x=Gy$ by an optimal inverse $G$ of $A$. This definition generalizes the earlier work of Foster (1961). Properties of optimal inverses are studied and some applications are discussed.

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